Marginally Strictly Negative Imaginary Systems

This article revisits a fundamental question in negative imaginary (NI) systems theory: what is the weakest viable notion of strictness that still preserves the classical feedback stability picture? To address this question, we introduce the notion of marginally strictly negative imaginary (MSNI) systems to accommodate simple nonzero imaginary‐axis poles while preserving strictly negative imaginary behavior away from those poles. An MSNI system is defined as the parallel interconnection of a lossless NI system and a strictly negative imaginary system. The proposed notion provides a less restrictive strictness framework suited for resonant control within NI systems theory. A new stability test is then developed for the positive feedback interconnection of a stable NI system and an MSNI system. The proposed test is stated in terms of the well‐known loop DC‐gain condition together with easily verifiable pointwise assumptions at the imaginary‐axis pole locations. A numerical example illustrates the validity of the condition and its effectiveness under resonant tracking requirements.